Removing noise caused by artifacts from a digital image signal

ABSTRACT

Noise in digitized image data is reduced by providing an array of pixels for each of which a gray level has been determined. For each column of the array, a distribution of gray levels is derived, and a range of acceptable gray levels is set based on the distribution. For pixels with a gray level outside the range, the gray level is changed to reduce the influence of noise in the imaged data.

This application is a continuation of application Ser. No. 09/186,494filed Nov. 4, 1998 now U.S. Pat. No. 6,295,384.

FIELD OF THE INVENTION

The invention is directed to improving the output obtained from animaging system and, in particular, to a technique which processes adigitized image of an object to remove noise.

BACKGROUND OF THE INVENTION

Imaging systems are used in such fields as microelectronics, medicine,biology, genetic engineering, mapping and even astronomy. The imagingdevice can be a suitable type of microscope or, in the case ofastronomy, a telescope. The demand for image accuracy is high and,therefore, the influence of noise in a signal derived from an imagedobject must be minimized.

For reasons of convenience and efficiency, the invention will bedescribed in the microelectronics environment, although anotherenvironment could also have been chosen. During the manufacture of verylarge scale integration (VLSI) semiconductor devices, measurements aremade at several stages of the manufacturing process to determine whetherparticular features on the object are within specified designtolerances. If not, then suitable corrective action is taken quickly.

As is well known, such a manufacturing process produces a wafer which isdivided into dies. Each die has a large number of electronic components.These components are defined by what can generally be termed “features”in the sense that a feature is detectable by a microscope as aforeground element distinguishable from a background, or vice versa, andhaving a dimension such as width. To measure that width the edges of thefeature must be located accurately. “Edge” is a term used to signifydetectable discontinuities in a signal obtained by imaging the feature(in any environment, not only microelectronics). The goal of edgedetection is to accurately locate the transitions despite the influenceof blurring and the presence of noise.

As technology has succeeded to increase the component density per die,the feature dimensions have shrunk to significantly below a micrometer.Consequently, the measurement equipment must measure submicrometerdimensions with lower allowable error tolerances.

Automated systems have been developed for making these measurements toreplace manual systems in order to obtain higher process yields, toreduce exposure of the wafers to contamination and to provide a higherthroughput. One example of an automated system is disclosed in U.S. Pat.No. 4,938,600. As shown in FIG. 1 which is taken from that patent, animage of a feature is recorded through a microscope and the recordedimage is then processed electronically to obtain the requiredmeasurements. One such automated system is the Model IVS-120 metrologysystem manufactured by Schlumberger Verification Systems of Concord,Mass., a division of Schlumberger ATE Products. The major elements ofthe system, including a wafer handler, an optical system and a computersystem, are mounted in a cabinet (not shown).

The wafer handler includes a cassette wafer holder 12 which containswafers to be measured, a prealigner 14, a wafer transport pick mechanism(not shown) for moving the wafers and a measurement stage 18 which holdsthe wafers during the actual measurement operation. During operation,the wafer transport pick mechanism removes a wafer 16 from cassette 12and places it on prealigner 14. Prealigner 14 then rotates wafer 16 to apredetermined orientation by sensing a mark, a flat spot or notched edgeon wafer 16, after which the wafer transport pick mechanism transferswafer 16 from prealigner 14 to measurement stage 18 and positions wafer16 in a horizontal orientation. Stage 18 is movable in three dimensionsfor precisely positioning wafer 16 relative to the optical system forperforming the actual measurement.

The optical system includes microscope 20 and video camera 22 positionedabove the measurement stage 18 and wafer 16. Microscope 20 typically hasa turret carrying several objective lenses providing a desired range ofmagnification and is mounted so that microscope 20 and camera 22 have avertical optical axis which is perpendicular to the wafer surface.

A feature to be measured on wafer 16 is located with microscope 20 in awell known manner by moving stage 18 until the feature is in the fieldof view of the objective lens. The optical system is focused, and afocused image of the feature is digitized and recorded by the camera 22.The image is then stored or “frozen”.

The system is controlled by a computer 30. Coupled to the computer 30are a monitor 32 for display of the image recorded by the camera 22 andtext, and a keyboard 36 (which constitute an input terminal for enteringoperator commands) and a disk drive 38 for storing system software anddata.

Image processor 28 uses software algorithms to locate the edges of theselected feature and make a measurement. Computer 30 then displays themeasurement data on screen 32, prints a hard copy or transfers the datadirectly to a host computer (not shown) for centralized data analysis.Once the process is complete, wafer 16 is returned to cassette 12 by thewafer handler.

The just-described system performs its task of edge detection very well.Image processor 28 determines where a discontinuity occurs in the graylevel of the digitized image. Such a discontinuity can occur for any oneof many well known reasons to create an edge of a feature. For example,an edge can occur where two materials meet which have different graylevels, or due to topology of the imaged surface. However, as is wellknown, the digitized image is subject to spurious noise from varioussources. For example, variations in the gray level due to noise can becaused by surface imperfections on the die, such as spots and cracks.This noise in the imaged signal can have a significant distortinginfluence on the accuracy with which the edge is detected, particularlywith the ever increasing precision which such automated measurementsystems must provide. (Of course, in environments other thanmicroelectronics, there are analogous causes of noise.)

Certain approaches are known which aim to eliminate the noise created bythese imperfections and thereby improve the signal-to-noise ratio (S/N).For example, smoothing filters are commonly used for noise reduction.However, as explained in Digital Image Processing by Gonzales and Woods,Addison-Wesley Publishing Co. 1993 at page 191, a smoothing filter blursedges because it relies on neighborhood averaging which averages all thepixels in an area of selected size around a pixel of interest. Such ablurring of the edge cannot be tolerated in a measurement system whichmust locate the edge precisely. For such an application, the authorsrecommend an alternative approach which uses median filters. Thisapproach replaces the gray level of each pixel by the median of the graylevels in a neighborhood of that pixel, instead of by the average. Thismethod is particularly effective to preserve edge sharpness when thenoise pattern includes strong, spike-like components. However, evenmedian filtering is not satisfactory for the type of precisionmeasurements discussed above because when the filter parameters are setto provide filtering, the edge gets modified, and when the parametersare set to preserve the edge, the filtering effect is reduced or eveneliminated.

SUMMARY OF THE INVENTION

One object of the present invention is to remove the influence of noisein a signal obtained with an imaging system.

A further object of the present invention is to improve the S/N ratio ofthe output signal received from the imaging device in such system.

Another object of the present invention is to enable improved accuracyfor a high precision measurement system which uses an imaging device.

Yet another object of the present invention is to enable improvedaccuracy of edge detection with an imaging system despite the presenceof noise in the image signal.

These and other objects are attained in accordance with one aspect ofthe present invention for reducing noise in a signal obtained by imagingan object with an imaging device. Digitized image data is providedcorresponding to an area of the object and having values of an imagingparameter for an array of m×n pixels. For each of columns n in thearray, a distribution of the number of pixels vs. imaging parameterlevel is derived. Based on the distribution, a range of acceptablevalues of imaging parameter levels is set. For all values of imagingparameter levels outside of the range, characteristics of the pixelsassociated with such values are changed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a prior art automated measurement systemfor providing optical measurements of a semiconductor device.

FIG. 2 is a schematic representation of an object with arectangular-shaped feature in the environment of microelectronics, adimension of which is to be measured.

FIG. 3 is a table of pixel gray levels produced from imaging the featureof FIG. 2.

FIG. 4 is a histogram of the pixel gray levels for one column of thetable of FIG. 3.

FIG. 5 is a schematic representation of a multiple-sided feature shapeddifferently from the one shown in FIG. 2.

FIG. 6 is a schematic representation of a circular-shaped feature.

FIG. 7 is a flowchart of the steps performed in accordance with theinvention to detect an edge.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

FIG. 2 illustrates a feature 50 on a surface 52 which constitutes a partof a sample, or object, being measured. Camera 22 utilizes a 16 bit graylevel signal to digitize the image from the microscope, thus providing acommensurate number of possible gray levels. For the sake ofillustration, feature 50 and surface 52 are presumed to have respectivegray levels of 100 (relatively dark) and 200 (relatively light). If thewidth of feature 50 is to be measured, it can be determined as thedistance between its edges 53 and 53 a. In order to locate the edge 53,i.e., the discontinuity from 200 to 100, a region of interest 54 is setby the operator to encompass the edge. The size of the region ofinterest, in terms of pixels, is set by the operator based on certaincriteria. For example, these criteria include the size of the feature,providing sufficient extra area to ensure capture of the feature, andobtaining sufficient data to perform the required processing fully andproperly. It is possible that several regions of interest 54 will bespaced along the entire length of edge 53 for various reasons, asexplained below.

The edge 53 is visible to the operator on image monitor 32 (FIG. 1) byapplying a prior art approach such as is available on the IVS-120. Thus,the position of edge 53 at this point is subject to the inaccuracy ofsuch approach due to noise, as discussed above, but it has sufficientaccuracy to enable the operator to set the region of interest 54 so thatthe present invention can be applied, as explained below.

Feature 50 and its surroundings on surface 52 are imaged by the imagingdevice, such as by microscope 20 in FIG. 1, and in accordance with step110 in FIG. 7. The resulting output is digitized, such as by camera 22in FIG. 1, and in accordance with step 112 in FIG. 7. In step 114 theoperator establishes the region of interest, as explained above, and thedigitized data therefor is obtained in step 116.

FIG. 3 shows a depiction of the area of interest 54 as a row and columnarray 55 of m×n pixels 56. Moreover, the array 55 is also shown with thedigitized image data of the gray level value for each pixel which isobtained in step 116.

FIG. 2 shows a dark spot 58 and a crack 60 on surface 52, both of whichare presumed to produce a darker gray scale level of 150. Spot 58 isrepresented in FIG. 3 by the pixel located at col. 3, row 3. Crack 60 isrepresented in FIG. 3 by the pixels at col. 1, row 7; col. 2, row 8; andcol. 3, row 9. Also, dark spot 61 coincides with edge 53. Edge 53 isrepresented on FIG. 3 by column 52, and spot 61 is represented by thegray level value of 75 at row 5 of that column. It should be readilyapparent that the width of crack 60 and the diameter of the spots likelycovers many pixels, not just one. Moreover, even if the spot 58, forexample, is so small that it corresponds in size to only one pixel andby coincidence the pixel is in perfect registration with it, the graylevels of the surrounding pixels may nevertheless also be affected bythe spot to have a gray level below 200 if the resolution of themicroscope optics results in a blur circle larger than the pixel size.It should be realized that the array 55 of pixels 56 in FIG. 3 has beenpresented for illustrative purposes in order to simplify the task ofexplaining the invention, and does not necessarily depict such graylevels accurately.

The invention will now proceed to process the digitized image data ofarray 55 in order to reduce the noise created by spots, cracks and otherartifacts in surface 52. This processing can be implemented by animprovement of image processor 28 or carried out by computer 30, forexample. The processing determines the mean value {overscore (X)} andthe standard deviation α for each column of array 55. Various well knowncomputational methods can be used. One approach will now be described inconnection with FIG. 4. FIG. 4 is a graph of a histogram which isderived from the values in one column of FIG. 3. If a range of 256 graylevels is selected for use, then gray levels 0-255 are along the x-axisand the number of pixels for each gray level is along the y-axis. Aswill be explained in more detail below, such a graph is derived for eachand every column of the pixel array 55. FIG. 4 has been derived fromcolumn 1 of FIG. 3. Preferably, the processing proceeds sequentially,column-to-column, starting at one side of the array, proceeding in adirection toward the edge of interest, and then on through to the otherside of the array. Thus, in the case of edge 53 as shown in FIG. 2, theanalysis begins at the left-most column (i.e., column 1) of array 55 andproceeds on through to column n.

As is readily apparent from FIG. 4, the graph has a primary peak at thegray level of 200 and a secondary peak at the gray level of 150. Thesecondary peak constitutes noise caused by the cracks and spots whichdistorts the gray levels corresponding to surfaces 50 and 52 and,therefore, affects the derived image and the accuracy with which theposition of edge 53 can be detected.

In accordance with the present invention, the mean value {overscore (X)}and the standard deviation a are calculated in a well known way, detailsof which are not deemed necessary to provide. A range of acceptable datahaving a boundary limit BL on either side of the mean value {overscore(X)} is then selected in accordance with step 122. A general equation toexpress how BL is derived is: BL={overscore (X)}±aσ, where “a” is aconstant selected by the operator when the apparatus is calibrated. Theselection of “a” is made per step 118 based on various factors which inthe operator's judgment and experience affect the accuracy of theresult. For example, if the edge is strongly distinctive and the noiseis weak, the “a” selected may be different than if the edge is not verydistinctive and the noise is strong. Likewise, for some conditions the“a” may be different for those pixels which are on one side of the meanvalue {overscore (X)} than for those pixels which are on the other side.Also, a BL on only one side of the mean value {overscore (X)} can beused. Some trial and error may be relied upon by the operator in makingthese choices.

In the example shown in FIG. 4, the operator will set “a” so that BLfalls at the root of the histogram or the root can be locatedautomatically by well known computational methods. For example, if themean value {overscore (X)} for column 1 happens to be 190 the standarddeviation σ happens to be 10 and the root is at 170, then “a” is set at2 in step 118. The range is defined by step 122 to be between a lowerboundary limit BL of 170 and an upper boundary limit of 210. Of course,these values are merely illustrative, and it should be understood thatthe shape of the primary and secondary peaks, together with the valuesof {overscore (X)} and σ, and the position of the boundary limitsrelative to such peaks can vary. However, such variations are stillhandled in accordance with the present invention, further details ofwhich will now be provided.

A detailed description of how the data in array 55 is processed will beprovided only with respect to gray levels below the lower BL (i.e. 170)which, hereinafter, will be referred to simply as BL. It should beunderstood that gray levels above the upper BL (i.e. 210) can beprocessed in an analogous manner.

In accordance with one approach of the present invention (step 124),every gray level in column 1 which falls below 170 is replaced by thegray level of the BL (i.e., values below 170 are replaced by 170). Inaccordance with another approach of the invention (also represented bystep 124, gray levels below BL are replaced with the gray level{overscore (X)} of the mean, i.e., by 190. Whether one or another ofthese approaches is picked depends upon which is found by the operatorto yield the better result under the particular circumstances involved.For whichever approach is used, the invention processes column 1 ofarray 55 and makes the necessary replacements of gray levels.

In accordance with yet another approach of the present invention (step126 which is shown to be an alternative by use of dotted lines), thosegray levels below BL represent invalid data. The invalid data isrejected from further image processing by removing each pixel involvedand its gray level. Thus, if a column has m pixels in it, and two ofsuch m pixels have gray levels below 170, then further processing of thecolumn data considers the column to have only m−2 pixels, and the grayscale levels of those two pixels are ignored. Further, processing isthen carried out with this data, as explained below. This approach doesnot reduce the visible artifacts, but it does provide data cleared ofinvalid information, which data can be usefully relied on for certainpurposes. Also, this approach is faster to process because it does notrequire gray level replacement.

A variation of this last approach is to use the m−2 (as used in theexample above) pixels for recalculating the mean value {overscore (X)},and then to use such recalculated value for replacing the gray level inthe two rejected pixels. Those pixels, with the replaced gray level, canthen be used to provide an image.

Per steps 120, 128 and 130, the above-described steps begin with column1 and are repeated for each and every one of the n columns of pixelarray 55. As a result, the influence of noise in the digitized imagedata of array 55 will have been reduced so that a sharp and cleardiscontinuity should be discernible in the rows which accurately depictsthe position of the edge as the pixel location(s) where the gray leveldrops from the vicinity of 200 to the vicinity of 100.

If the length of an edge is divided into several areas of interest inorder to, for example, keep the amount of data to a manageable amount,then the above-described processing is performed until the digitizeddata in all such portions has been processed. Conversely, several areasof interest can be processed together.

Once the gray levels for the pixels in column 1 have been set inaccordance with any one of the above-described approaches, an averagegray level for all or part of column 1 is calculated from the sum of thegray scale values divided by the number of pixels. Whether all or partof a column is used depends on the particular circumstances, such as thenature of the feature, the amount of data in the column. This averagingis repeated for all of the columns to derive an averaged row which has adiscontinuity corresponding to the location of the edge. Step 132represents this averaging operation as well as other edge detectionoperations. The edge detected in this way will represent the edgeposition for the entire region of interest, or portion thereof, whichwas used to process the data from which the edge is detected. Details ofhow the edge is located with the above-described processed digitizedimage data are not provided because they do not form a part of theinvention and are deemed to be within the knowledge of one with ordinaryskill in the art. Chapter 7 of the above-mentioned Digital ImageProcessing book has a section on edge detection which is herebyincorporated by reference. As explained above, the invention is directedtoward reducing the effect of noise in the digitized image data obtainedwith the imaging device (which can be a microscope, telescope, etc.).

FIG. 2 shows a rectangular-shaped feature of the object, the width ofwhich is being measured and having both of its sides 53 and 53 a inparallel. However, the present invention is applicable to anymulti-sided geometric shape. The key to using the present invention isto set up region of interest 54 such that its columns of pixels 56 areparallel to the edge of immediate interest. For example, FIG. 5 shows anoctagon 65 on surface 52. Region of interest 67 is set up to locate edge69 by conducting the processing of pixel columns from left to right, inthe same way as described above with respect to FIGS. 2 and 3. Likewise,region of interest 71 is set up to locate edge 73 by conducting theprocessing of pixel columns in the direction of arrow 75. The definitionof “column” in this sense is not just a vertical sequence of pixels but,rather, a set of pixels in a straight line all of which are spaced anintegral number of pixels from edge 73. Thus, if region of interest 71is sized to begin the analysis at a column ten pixels away from edge 73,then “column” 1 to be analyzed will include all the pixels in the m rowsof region of interest 71 which are 10 pixels from edge 73.

The spacing of the columns described above is one pixel. However, it isalso possible to use sub-pixel and multiple pixel column spacing. Thus,if a spacing of one-half pixel is used, then the narrower spacingresults in pixels with more similar gray levels in each column. Aspacing of 2 pixels can also be used, and such wider spacing results ina faster processing time.

Not only can the present invention be applied to multi-sided geometricalshapes of a feature, it can also be applied to curved edges. Forexample, FIG. 6 shows a circle 80 representing a circular feature andportions of concentric circles 79, 81 and 82 having respective radiiwhich are one pixel apart (for reasons explained below).

The steps of FIG. 7 can be applied to circle 80. In particular, arectangular region of interest 100 is defined. As explained before, asuitably sized region of interest 100 is selected by the operator. A“column” is then selected to have a width based on a pre-defined spacingfrom the circle. The spacing could be the size (e.g. width) of a pixel,for example. For purposes of this explanation, let us call the columnclosest to circle 80 column 1, the next one column 2, and so on. Each ofthe pixels is also numbered.

The operator of a machine can pick the criteria in accordance with whichto associate any given pixel with a particular column, or this can beotherwise preset. Examples of such criteria are whether any part of thepixel falls in a column, whether most of a pixel falls in a column,whether more than a fixed fraction falls in a column, or whether all ofa pixel falls in a column. For purposes of illustration, the followingTables A and B have been prepared based on the first and secondabove-mentioned criteria, respectively.

TABLE A Col. 1 Col. 2 1  9 2 10 3 11 5 13 6 14 7 15 8 16 9 17 10  18 11 19 12  20 13  21 14  22 15  23 16  24

TABLE B Col. 1 Col. 2  1  9  2 15  7 16  8 18 10 19 11 20 12 21 13 22 1423

Table A provides more data per column, but with some overlap since somepixels are used in more than one column. Table B provides less data percolumn, but with little or no overlap. Whether one option or another isselected depends on what the operator regards as producing superiorresults.

The spacing from circle 80 to define the columns need not be based onthe dimensions of one pixel. The spacing can be on a sub-pixel level oron a multiple-pixel level. The above-described “column” approach used inFIG. 6 is also applicable to any shaped curve. The boundary of eachcolumn follows the shape of the curve at a specified multiple of theselected spacing from the curve. The analysis of pixels and their graylevels within such region of interest proceeds in the same way asdescribed above in connection with FIGS. 2 and 3.

Although preferred embodiments of the present invention have beendescribed in detail above, various modifications thereto will be readilyapparent to anyone with ordinary skill in the art. For example, thefeature can be imaged with any imaging device having an output which canbe digitized to produce a plurality of gray levels, such as particlebeam (e.g. SEM), optical system (e.g. microscope), scanned probe (e.g.STM, AFM), telescope, camera (e.g. satellite), MRI and so on.Furthermore, it is not necessary to have a separate unit for the imageprocessor 28 and computer 30. These can be combined. Also, processor 28or any other computational device can handle the processing. It mustalso be noted that although gradations in the digitized image aredescribed above as being represented by gray levels, this is not theonly usable imaging parameter. An imaging parameter, of which gray levelis but one example, can also be a Z-dimension output signal produced byany type of scan probe microscope, by way of another example. The typeof imaging parameter used depends at least in part on the imaging deviceselected for the machine. These and all other such variations areintended to fall within the scope of the present invention as defined bythe following claims.

I claim:
 1. A method for measuring a physical feature of an object byaccurately determining a position of an edge of the feature in adigitized image of at least a portion of the object, comprising:locating an approximate position of the edge; providing digitized imagedata corresponding to a selected area of the object which encompassessaid approximate position of the edge and having respective values of animaging parameter for pixels within said area; deriving an array of m×nimaging parameter values corresponding to pixels arranged in a pluralityof columns n each of which is spaced from said approximate position ofthe edge by a specified distance; setting a range of acceptable valuesof said imaging parameter; replacing all values of said imagingparameter in said array that are outside said range with a designatedvalue to obtain a revised array of imaging parameter values; andaccurately determining said position of the edge from said imagingparameter values in the revised array; wherein setting a range ofacceptable values of said imaging parameter comprises: for each ofcolumns n, deriving a distribution of the number of pixels vs. imagingparameter values; and based on the distribution, setting said range ofacceptable values of the imaging parameter.
 2. The method of claim 1,wherein said columns n are respectively spaced from the approximateposition of the edge by an integral number of pixels.
 3. The method ofclaim 1, wherein said columns n are respectively spaced from theapproximate position of the edge by an integral number of sub-pixels. 4.The method of claim 1, wherein said columns n are respectively spacedfrom the approximate position of the edge by an integral number ofmulti-pixels.
 5. The method of claim 1, wherein the imaging parameter isgray level.
 6. The method of claim 5, wherein the replacing stepcomprises replacing the gray levels that are outside said range with adesignated gray level.
 7. The method of claim 6, further comprising thestep of deriving a mean value of the gray levels in a column, andwherein said designated gray level is said mean value.
 8. The method ofclaim 6, wherein said designated gray level is the gray level at aboundary of said range.
 9. The method of claim 8, wherein said rangesetting step comprises: determining a mean value; determining a standarddeviation; and setting a boundary of said range at a difference fromsaid mean value related to said standard deviation.
 10. The method ofclaim 1, wherein said step of replacing imaging parameter values toobtain a revised array comprises deleting imaging parameter values thatare outside of said range from said digitized image data.
 11. The methodof claim 1, wherein said edge detecting step comprises identifyingdiscontinuities in values of the imaging parameter between adjacentcolumns of the revised array.
 12. The method of claim 1, wherein saidedge is linear and said columns are correspondingly linear.
 13. Themethod of claim 1, wherein the approximate position of said edge isarcuate, and said columns are correspondingly arcuate.
 14. A method formeasuring a physical feature of an object by accurately determining aposition of an edge of the feature in a digitized image of at least aportion of the object, comprising: locating an approximate position ofthe edge; providing digitized image data corresponding to a selectedarea of the object which encompasses said approximate position of theedge and having respective values of an imaging parameter for pixelswithin said area; deriving an array of m×n imaging parameter valuescorresponding to pixels arranged in a plurality of columns n each ofwhich is spaced from said approximate position of the edge by aspecified distance; setting a range of acceptable values of said imagingparameter; replacing all values of said imaging parameter in said arraythat are outside said range with a designated value to obtain a revisedarray of imaging parameter values; and accurately determining saidposition of the edge from said imaging parameter values in the revisedarray; wherein said step of setting a range of acceptable valuescomprises deriving a first mean value of the imaging parameter based onall values in a column, and wherein said replacing step comprisesderiving a second mean value based only on values within said range andreplacing the values outside said range with said second mean value. 15.Apparatus for measuring a physical feature of an object by accuratelydetermining a position of an edge of the feature in a digitized image ofat least a portion of the object, comprising: means for locating anapproximate position of the edge; means for providing digitized imagedata corresponding to a selected area of the object which encompassessaid approximate position of the edge and having respective values of animaging parameter for pixels within said area; means for deriving anarray of m×n imaging parameter values corresponding to pixels arrangedin a plurality of columns n each of which is spaced from saidapproximate position of the edge by a specified distance; means forsetting a range of acceptable values of said imaging parameter; meansfor replacing all values of said imaging parameter in said array thatare outside said range with a designated value to obtain a revised arrayof imaging parameter values; and means for accurately determining saidposition of the edge from said imaging parameter values in the revisedarray; wherein said means for setting a range of acceptable values ofsaid imaging parameter comprises: means for deriving, for each ofcolumns n, a distribution of the number of pixels vs. imaging parametervalues; and means for setting, based on the distribution, said range ofacceptable values of the imaging parameter.
 16. The apparatus of claim15, wherein said columns n are respectively spaced from the approximateposition of the edge by an integral number of pixels.
 17. The apparatusof claim 15, wherein said columns n are respectively spaced from theapproximate position of the edge by an integral number of sub-pixels.18. The apparatus of claim 15, wherein said columns n are respectivelyspaced from the approximate position of the edge by an integral numberof multi-pixels.
 19. The apparatus of claim 15, wherein the imagingparameter is gray level.
 20. The apparatus of claim 19, wherein themeans for replacing comprises means for replacing the gray levels thatare outside said range with a designated gray level.
 21. The apparatusof claim 20, further comprising means for deriving a mean value of thegray levels in a column, and wherein said designated gray level is saidmean value.
 22. The apparatus of claim 20, wherein said designated graylevel is the gray level at a boundary of said range.
 23. The apparatusof claim 15, wherein said range setting means comprises: means fordetermining a mean value; means for determining a standard deviation;and means for setting a boundary of said range at a difference from saidmean value related to said standard deviation.
 24. The apparatus ofclaim 15, wherein said means for replacing imaging parameter values toobtain a revised array comprises means for deleting imaging parametervalues that are outside of said range from said digitized image data.25. The apparatus of claim 15, wherein said means for setting a range ofacceptable values comprises means for deriving a first mean value of theimaging parameter based on all values in a column, and wherein saidreplacing means comprises means for deriving a second mean value basedonly on values within said range and replacing the values outside saidrange with said second mean value.
 26. The apparatus of claim 15,wherein said edge detecting means comprises means for identifyingdiscontinuities in values of the imaging parameter between adjacentcolumns of the revised array.
 27. The apparatus of claim 15, whereinsaid edge is linear and said columns are correspondingly linear.
 28. Theapparatus of claim 15, wherein the approximate position of said edge isarcuate, and said columns are correspondingly arcuate.